TY - JOUR
T1 - The weak completion semantics and equality
AU - Saldanha, Emmanuelle Anna Dietz
AU - Hölldobler, Steffen
AU - Schwarz, Sibylle
AU - Stefanus, Lim Yohanes
N1 - Publisher Copyright:
© 2018, EasyChair. All rights reserved.
PY - 2018
Y1 - 2018
N2 - The weak completion semantics is an integrated and computational cognitive theory which is based on normal logic programs, three-valued ̷Lukasiewicz logic, weak completion, and skeptical abduction. It has been successfully applied – among others – to the suppression task, the selection task, and to human syllogistic reasoning. In order to solve ethical decision problems like – for example – trolley problems, we need to extend the weak completion semantics to deal with actions and causality. To this end we consider normal logic programs and a set E of equations as in the fluent calculus. We formally show that normal logic programs with equality admit a least E-model under the weak completion semantics and that this E-model can be computed as the least fixed point of an associated semantic operator. We show that the operator is not continuous in general, but is continuous if the logic program is a propositional, a finite-ground, or a finite datalog program and the Herbrand E-universe is finite. Finally, we show that the weak completion semantics with equality can solve a variety of ethical decision problems like the bystander case, the footbridge case, and the loop case by computing the least E-model and reasoning with respect to this E-model. The reasoning process involves counterfactuals which is necessary to model the different ethical dilemmas.
AB - The weak completion semantics is an integrated and computational cognitive theory which is based on normal logic programs, three-valued ̷Lukasiewicz logic, weak completion, and skeptical abduction. It has been successfully applied – among others – to the suppression task, the selection task, and to human syllogistic reasoning. In order to solve ethical decision problems like – for example – trolley problems, we need to extend the weak completion semantics to deal with actions and causality. To this end we consider normal logic programs and a set E of equations as in the fluent calculus. We formally show that normal logic programs with equality admit a least E-model under the weak completion semantics and that this E-model can be computed as the least fixed point of an associated semantic operator. We show that the operator is not continuous in general, but is continuous if the logic program is a propositional, a finite-ground, or a finite datalog program and the Herbrand E-universe is finite. Finally, we show that the weak completion semantics with equality can solve a variety of ethical decision problems like the bystander case, the footbridge case, and the loop case by computing the least E-model and reasoning with respect to this E-model. The reasoning process involves counterfactuals which is necessary to model the different ethical dilemmas.
UR - http://www.scopus.com/inward/record.url?scp=85068403198&partnerID=8YFLogxK
U2 - 10.29007/pr47
DO - 10.29007/pr47
M3 - Conference article
AN - SCOPUS:85068403198
SN - 2398-7340
VL - 57
SP - 326
EP - 342
JO - EPiC Series in Computing
JF - EPiC Series in Computing
T2 - 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, LPAR 2018
Y2 - 17 November 2018 through 21 November 2018
ER -